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How to compare saturated model to baseline model?


Asked by Barbara Solomon on Dec 08, 2021 FAQ



To test how well our model compares to a saturated model, we compute chi-square as follows, minus two times the differences in the log likelihoods; -2* (-2949.3343 – -2943.2087) = 12.2512. The degrees of freedom for this chi-square is the difference in the number of parameters estimated in the two model (20 – 15 = 5).
Accordingly,
To test how well our model compares to a saturated model, we compute chi-square as follows, minus two times the differences in the log likelihoods; -2* (-2949.3343 – -2943.2087) = 12.2512. The degrees of freedom for this chi-square is the difference in the number of parameters estimated in the two model (20 – 15 = 5).
Consequently, The baseline model. So, that brings us to the baseline model. This is defined in the Stata [SEM] Structural Equation Modeling Reference Manual as a model which includes the means and variances of all observed variables plus the covariances of all observed exogenous variables.
Furthermore,
Since there is only one observed exogenous variable, female, in our model, there will be no covariances in our baseline model. For the baseline model we estimated 10 parameters; 5 variances and 5 means. In comparing this model with the saturated model there was a difference of 10 degrees of freedom, 20 – 10 = 10.
Keeping this in consideration,
You can compute the number of parameters in a saturated model of k observed variables by the formula k* (k+1)/2 + k. In our example, it is 5* (5+1)/2 + 5 = 20. The log likelihood for this model is -2943.2087. To test how well our model compares to a saturated model, we compute chi-square as follows,...